Give the tests their own database and drop the template specs

pytest was deleting every user on teardown against the development
database. The engine is built at import time, so tests/__init__.py pins
POSTGRES_DB before app.core.config loads; the fixture creates the schema
and drops the database again, guarded against a name that is not _test.

Playwright now defaults at the integrated stack, which is the origin the
API allows, so a bare `bunx playwright test` works without a dev server.
The four template specs that asserted copy we no longer ship are gone,
along with the helpers they were the last callers of. The admin edit
assertion was page-wide and only ever passed on a fresh database.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01KkmeRiyeYmVZqJVwuyHq9o

frontend/tests/utils/user.ts

@@ -1,21 +1,5 @@
 import { expect, type Page } from "@playwright/test"
 
-export async function signUpNewUser(
-  page: Page,
-  name: string,
-  email: string,
-  password: string,
-) {
-  await page.goto("/signup")
-
-  await page.getByTestId("full-name-input").fill(name)
-  await page.getByTestId("email-input").fill(email)
-  await page.getByTestId("password-input").fill(password)
-  await page.getByTestId("confirm-password-input").fill(password)
-  await page.getByRole("button", { name: "Sign Up" }).click()
-  await page.goto("/login")
-}
-
 export async function logInUser(page: Page, email: string, password: string) {
   await page.goto("/login")
 
@@ -27,9 +11,3 @@ export async function logInUser(page: Page, email: string, password: string) {
     page.getByText("Welcome back, nice to see you again!"),
   ).toBeVisible()
 }
-
-export async function logOutUser(page: Page) {
-  await page.getByTestId("user-menu").click()
-  await page.getByRole("menuitem", { name: "Log out" }).click()
-  await page.goto("/login")
-}